At the fuses we are measuring offset voltage. That is measured from one end of the fuse to ground. We are assuming the fuse is good

.
Did you really measure across the fuse?
And since you mentioned TR03 and TR04 that tells me you did not remove the driver board first.
That said what specifically what voltages are jumping around, E, B, C?
By having the driver board out I am hoping to confirm the output transistors are OK and with the inputs to the protection circuit protection being zero volts that the protection circuit pulls the relay in.
If that takes place the problem area becomes the driver board and maybe it's power supplies.